In a systematic sample, the only samples possible are those including every k^th item from the random starting position.
Simple random sampling otherwise called probability sampling involves selecting a subset of a part of a population in which each member of the population has equal chances of being selected while systematic sampling involves the use of sampling interval which is determined by dividing the population by the sample size and a random starting point is selected. for example let say we have a population of 1000 people and we want to systematically select 50 people, 1000 / 50 = 20, it means after choosing a random starting point, we select every 20th person after the starting point until the desire sample size has been attained.
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How do you write an equation in slope-intercept form of the line that is perpendicular to a graph?.
The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.
The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.
The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.
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How is the area of a triangle formed by the Midsegments of a triangle related to the area of the original triangle use an example to justify your answer?.
A triangle's midsegment is the section created by joining any two of its sides at their midpoints.
Simply said, it equally splits the two triangle sides. A side is divided into two equal segments at its halfway. The middle segment of the triangle ABC is DE, as shown in the image below. Segment AB is divided into two equal portions at point D, and segment CB is divided into two equal parts at point E. The base of the triangle is the side on which the midsegment does not meet. The segment created by joining the midpoints of a trapezoid's two legs is known as the midsegment. Despite the fact that a trapezoid's midsegment is also helpful
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Calculate length of bc
Answer:
a) BC = 8.66
b) BC = 4.33
Step-by-step explanation:
a)
solution:
cos30°=BC/AC
or, BC=0.866*10
BC=8.66
b)
solution:
BC=5*0.866
BC=4.33
The number of miles driven by Zoe is directly proportional to the number of gallons
she used.
Number of Gallons Used
9
28
40
Number of Miles Driven
348.3
1083.6
1548
How many miles would she drive on 47 gallons?
Answer:
1818.9 mi
Step-by-step explanation:
If the num of miles is directly proportional, then we can find out that she drives 348.3/9 = 38.7 mi/gal (this also works for the other two pairs)
To find the distance with 47 gallons, you multiply 38.7 by 47, to get 1818.9 mi.
The players on a basketball team decided that they wanted
to score 750 points by the end of the season. The coach
promised pizzas if the team scored within 50 points of its
goal. Solve the inequality |x - 750| ≤ 50, which represents
the total possible number of points the team could score to earn pizzas.
The total possible number of points the team could score to earn pizzas is 700, using the inequality |x - 750| ≤ 50
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Based on the given conditions, formulate: 750 -50
Calculate the sum or difference will be 700
Hence, the inequality possible number of points the team could score to earn pizzas is 700
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A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
O (x,y) - (x + 5, y- 3)
O (x,y) - (x + 5, y + 3)
O (x,y) - (x-3,y +5)
O (x.y) - (x + 3, y +5)
The rule to describe the translation is (x , y) ---> ( x + 3 , y + 5 )
Translation is Changing scale , shifting or reflection of a parent figure.
Scale means Changing size and shape of figure
Shifting means moving the figure to new location this could be upwards downwards , left and right
Reflection means making a mirror image or figure to different quadrant or along different axis.
According to the question,
A rectangle on a coordinate plane whose coordinates are (x, y) is translated 5 units up and 3 units to left
Shifting a plane upwards means changing the y coordinates so ,
y +5
shifting towards left means shifting to left side of x - axis
so , x + 3
Hence , the rule to describe this translation is
(x , y) ---> ( x + 3 , y + 5 )
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what is 459.63? is it irrational?
Answer:
No it is not irrational
Step-by-step explanation:
459.63 is a rational number.
Irrational numbers are numbers that can't be shown as simple fractions
Examples of irrational numbers are:
√2, π(Pi), 0.45445544455544445555.. (because it doesn't end)
State the complementary event of rolling a die and getting a number less than 3.
The complementary event of rolling a die and getting a number less than three is that the six-sided die is rolled and the outcome is greater than three. Where P = n < 3 is the event and its complement is P' = n > 3.
What is the complement of an event?The sample space of all outcomes that are not the event in question is the complement of an event. The inverse of "a flipped coin lands on heads" is "a flipped coin lands on tails."
If the chance of drawing a red marble from a bag is 26%, the chance of the complement (picking a non-red marble ) is 74%.
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Which table represents the function y = -2x + 4?
Input x 0 1 2
Output y 4 7 10
Input x 0 1 2
Output y 4 2 0
Input x 0 1 2
Output y 4 6 8
Input x 0 1 2
Output y 3 4 5
The table that represents the function y = -2x + 4 is: the second table.
How to Find the Function that Represents a Table?Considering the third table representing a function given:
x | y
0 4
1 2
2 0
Find the slope (m) using the two points (1, 2) and (2, 0):
Slope (m) = change in y / change in x = (0 - 2) / (2 - 1)
m = -2/1
m = -2.
The y-intercept (b) = 4.
Substitute m = -2 and b = 4 into y = mx + b:
y = -2x + 4
Therefore, the second table represents the function y = -2x + 4.
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In the Bayesian linear model, the priors for the intercept and for the slope are independent. True or false: in the posterior distribution, the intercept and slope may be correlated. true or false?
(a) The statement about Bayesian model "For the Bayesian linear model, the priors for intercept and slope are independent" is False .
(b) The statement about posterior distribution "in posterior distribution, intercept and slope may be correlated" is False .
In the question ,
it is given that ,
Part(a) ,
the statement is given to be "In Bayesian linear model, the priors for the intercept and slope are independent" , we have to check whether the statement is True or False .
We have the linear model as [tex]y_{i}= \alpha +\beta x_{i} +A_{i}[/tex] , where [tex]A_{i}[/tex]≈N(0,σ²) , α is the intercept and β is the slope .
we know that priors [tex](\hat{\alpha } , \hat{\beta })[/tex] are not independent ,
Cov [tex](\hat{\alpha } , \hat{\beta })[/tex] = [tex]\frac{-\bar{x}}{S_{xx} }[/tex] *σ² ,
So , the priors for the intercept and for the slope are independent ,
hence the statement is False .
Part(b) ,
the statement is given to be "In posterior distribution, intercept and the slope may be correlated" ,
For Posterior distribution , as [tex]A_{i}[/tex]≈N(0,σ²) ,
and 2 + [tex]\beta x_{i}[/tex] is a non random part of the model ,
and Cov([tex](A_{i} , A_{i} )[/tex] = 0 for i ≠ j .
hence , we can say that the intercept and slope are not Corelated ,
the statement is False .
Therefore , both the given statement are False .
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What is the remainder when x3 1 is divided by x 1?.
The remainder when x³ + 1 is divided by x + 1 is 0
Given,
The polynomial functions; x³ + 1 and x + 1
We have to find the remainder when x³ + 1 is divided by x + 1
Polynomial function;-
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Here,
p(x) = x³ + 1
g(x) = x + 1 = 0
x = -1
Then,
p(x) = x³ + 1
p(-1) = -1³ + 1 = -1 + 1 = 0
That is,
The remainder when x³ + 1 is divided by x + 1 is 0
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A pendulum of length L cm has time period T seconds.
T is directly proportional to the square root of L.
The length of the pendulum is increased by 40%.
Work out the percentage increase in the time period.
The percentage increase in the time period is 6.3245%.
Given:
A pendulum of length L cm has time period T seconds.
T is directly proportional to the square root of L.
The length of the pendulum is increased by 40%.
Let L1 and T1 be the increased pecentage.
T α [tex]\sqrt{L}[/tex]
T/[tex]\sqrt{L}[/tex] = constant
T/[tex]\sqrt{L}[/tex] = T1/[tex]\sqrt{L1}[/tex]
T1 = [tex]\sqrt{L1}[/tex] * T/[tex]\sqrt{L}[/tex]
= [tex]\sqrt{L1/L}[/tex]* T
= [tex]\sqrt{40/100 *L / L}[/tex] * T
= [tex]\sqrt{0.4}[/tex] * T
= [tex]\sqrt{0.4} *100[/tex]
= 6.3245% T
Therefore The percentage increase in the time period is 6.3245%.
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how will the volume of the pyramid change if each side is multiplied by a factor of one-half?
Answer:
I think it will be one eighth times the volume
Step-by-step explanation:
Solve the following inequality: -4x
+ 14 ≤ 54
The solution to the inequality is solved as: x ≥ -10.
How to Solve an Inequality?To solve an inequality means to find the possible values of the variable in the inequality that will make it true.
Given the inequality:
-4x + 14 ≤ 54
Subtract 14 from both sides of the inequality:
-4x + 14 - 14 ≤ 54 - 14 [Subtraction property of equality]
-4x ≤ 40
Divide both sides by -4 then change the inequality sign:
-4x/-4 ≥ 40/-4 [division property of equality]
x ≥ -10
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a petty cahs fund was established with a $360 balance. it currently has cash of $42 and petty cash tickets totaling $318.
A credit to cash for $318 would be included in the entry to replenish the fund.
What is Balance?The balance is the sum owing on an account in banking and accounting. The term "balance" in accounting refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a certain financial period. The account shows a negative balance when total debits exceed total credits. There is just one rule in the balancing method: Perform the identical action on both sides of the equal sign so that only the unknown variable is left on one side.
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PLEASE HELP ME WITH THIS!
the base of a triangle is 4 meters shorts than its height. what are the height and base of the triangle if its area is 48 square meters?
Height and base of a triangle with given area 48 square meters is 12meters and 8 meters respectively.
As given ,
Area of the triangle = 48 square meters
Let 'y' meters represents the height of the triangle
Then 'y - 4' meters represents the base of a triangle.
Area of a triangle = ( 1/2 ) × base × height
Substitute the values we get
48 = ( 1 / 2) × ( y - 4 ) × y
⇒ 96 = y² - 4y
⇒ y² - 4y - 96 = 0
⇒ y² - 12y + 8y - 96 = 0
⇒ ( y - 12 ) ( y + 8 ) =0
⇒ y = 12 or y = -8
Height cannot be negative.
⇒y = 12meters
Base = 12 -4
= 8 meters
Therefore, height and base of a triangle with given area is 12 meters and 8 meters respectively.
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In a cla of 26 tudent 15 of them like math 13 of them like Englih and 9 of them don’t like math or Englih
Using Probability,
The probability that a randomly selected student in the class likes math or English is 11/26.
We have provided the following information,
total number of students in a class = 26
number of students who likes Math = 15
number of students who likes English = 13
number of students who does not likes English or Math = 9
let x be number of students who likes both of subjects .
firstly , we have to find out the value of x i.e total number of students who likes both subjects out of 26 students class .
For this , number of students who likes any one of subjects from both = 26- 9 = 17
but we have total 28 (i.e., 15 + 13 )students who likes Math and English.
so, number of students who likes only Math = 17-15 = 2
number of students who likes only English = 4
then, number of students who likes both subjects
(x) = 26 - 4- 2-9 = 11
randomly one student is selected from the Class,
The probability that a randomly selected student in the class likes math or English = 11/26
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Complete question:
In a class of 26 students: 15 like math, 13 like English, 9 does not like both. What is the probability that a randomly selected student in the class likes math or English?
There are currently 4000 mice in a population that grows continuously and exponentially. 10 years ago there were 100 individuals. How much longer (in years) will it take to reach 7000? round and give your answer to 2 decimal places
It will take approximately 11.62 years to reach a population of 7000 mice.
To solve this problem, we can use the formula for exponential growth:
[tex]\mathrm{N = N_0 \times e^{(r \times t)}}[/tex]
Where:
N = Final population size
N₀ = Initial population size
r = Growth rate
t = Time (in years)
Let's calculate the growth rate (r):
N₀ = 100
N = 4000
[tex]\mathrm{r = ln(N/N_0) / t}[/tex]
[tex]\mathrm {r = ln(4000/100) / 10}\\\\\mathrm {r = ln(40) / 10}\\\\\mathrm {r \approx 0.3688}[/tex]
Now, let's find the time required to reach 7000 mice:
[tex]\mathrm {N = 7000}\\\\\mathrm {t = ln(N/N_0) / r}[/tex]
[tex]\mathrm {t = ln(7000/100) / 0.3688}\\\\\mathrm {t \approx 11.52 \ years}[/tex]
Therefore, it will take approximately 11.62 years to reach a population of 7000 mice.
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Andre wants to make an open-top box by cutting out corners of a 22 inch by 28 inch piece of poster board and then folding up the sides. The volume v(x) in cubic inches of the open-top box is a function of the side length x in inches of the square cutouts.
The expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.
It is given that:
Andre wants to make an open-top box by cutting out the corners of a 22-inch by 28-inch piece of poster board and then folding up the sides.
As we know,
The volume of the box = length×width×height
V = (28 - 2x)(22 - 2x)(x)
Plug x = 2
V = (28 - 2×2)(22 - 2×2)(2)
V = (24)(18)(2) cubic inches.
V = 864 cubic inhces
Since x measures length, it is not possible for it to be smaller than zero. In addition, since the width of the box's bottom cannot be less than zero.
Thus, the expression for the volume is V = (28 - 2x)(22 - 2x)(x), and the volume of the box is 864 cubic inches.
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What is the slope of the line that passes through the points (-3, 3), and (1, -5)?
-1/2
2
1/2
-2
In preparing for the upcoming holiday season, fresh toy company (ftc) designed a new doll called the dougie that teaches children how to dance. the fixed cost to produce the doll is $100,000. the variable cost, which includes material, labor, and shipping costs, is $31 per doll. during the holiday selling season, ftc will sell the dolls for $39 each. if ftc overproduces the dolls, the excess dolls will be sold in january through a distributor who has agreed to pay ftc $10 per doll. demand for new toys during the holiday selling season is extremely uncertain. forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. the normal probability distribution is assumed to be a good description of the demand. ftc has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision. (a) determine the equation for computing ftc's profit for given values of the relevant parameters (e.g., demand, production quantity, etc.). using this equation, compute ftc's profit (in dollars) when realized demand is equal to 60,000 (the average demand).
The equation for ftc's profit is Profit = Sales – (Variable Cost + Fixed Cost)
According to the question,
The fixed cost to produce the doll = $100,000
Variable cost = $31
Selling price during holiday season = $39
Selling price during January = $10
Demand of new toys follows normal distribution
average sales = 60,000
Standard deviation = 15,000
Demand assumed in normal distribution = 60,000
The equation for ftc's profit ;
Let demand be d , production quality be p , fixed cost be x and variable cost be y
Maximum Profit:
Profit = Sales – (Variable Cost + Fixed Cost)
During the holiday season, For 40,000 dolls
Sales = 40,000 * 39 = $1,560,000
profit = $1,560,000 – (x+ y)
Variable Cost = 31*40,000 = 1,240,000
Fixed Cost = $100,000
Total Cost = 1,240,000+100,000 = $1,340,000
Profit = 1,560,000 – 1,340,000
= $220,000
Maximum Profit = $220,000
Average Profit: Off season sale price * Demand =$10*40,000
= $400,000
average sales = ($400,000 + 1,560,000 ) / 2=$1960,000/2
= $980,000
Average profit = 980,000 – 73,000= $972,700
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if speed varies inversely as the time it takes to drive and kris takes 5 hours driving at 55 mph, what speed will martin need to drive if he wants to take 512hours
The speed that will martin need to drive, if he wants to take the 512 hours is 0.537 mph.
What does proportionality's constant look like?Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.
Speed and travel time vary in opposite directions.,
So v ∝ 1/t.
speed = v
time = t
So
=> v = k/t, k=constant of proportionality.
Since it takes Kris 5 hours when driving at 55 mph,
=> v = 55mph and t = 5 hours.
=> 55 = k/5
by doing cross multiply
=> k = 55*5
=> k = 275
Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t
=> v = 275/512
=> v = 0.537 mph
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Anthony has 40 books, and Tommy has 50 books. If Vlad has twice as many books as Anthony and Tommy combined, then what does Vlad have?
A.) 180
B.) 90
C.) 245
D.) 115
Answer:
180
Step-by-step explanation:
first we combine what Anthony and Tommy have by adding
40+50
90
And twice as many is multiplying by 2
2x90
180
Hopes this helps please mark brainliest
Answer:180
explanation:40+50=90
90x2=180
Determine the value of b in the equation b3 = −125. b = −5 b = 5 b = −41.7 b = 41.7
The value of b in the equation [tex]b^{3}[/tex] = 125 will be 5. Option (b) is correct.
The question is about the system of equations. According to the question, we have the following equation:
b³ = 125.
We can find the value of b by simplifying and using the rules of equations.
First, we need to Factorize 125 on the right-Hand side, we get.
b³ = 5.5.5 = 5³
Hence we get,
b³ = 5³
We know that if there are two expressions that are equal and we add, subtract, multiply or divide into both sides of the equation, the resulting equation will also be equal. So, Multiply both sides by the cube root, and we get:
[tex]\sqrt[3]{b^{3}} = \sqrt[3]{5^{3}}[/tex]
[tex](b^{3})^{\frac{1}{3}} = (5^{3})^{\frac{1}{3}}[/tex]
[tex](b})^{\frac{3}{3}} = (5})^{\frac{3}{3}}[/tex]
[tex](b})^1 = (5})^1[/tex]
So we get the value of b = 5, hence the correction option will be (b).
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a rectangular room twice as long as it is wide would contain 145 square feet more if each side were one foot longer. what is the length of the room?
The length of the room will be 96 ft after increasing each side by 1 foot.
Let L be the length of the room and W be the width of the room.
Given , L = 2W.
Area , A = LW
= 2W × W
= 2W²
On increasing each side by 1 foot, new area is A' = (L + 1)(W + 1)
= (2W + 1)(W + 1)
= 2W² + 3W + 1
Since, the room would contain 145 ft more if each side were increased by 1 foot, then its new area is A' = A + 145 = 2W² + 3W + 1
2W² + 145 = 2W² + 3W + 1
145 = 3W + 1
3W = 145 - 1
3W = 144
W = 144/3
W = 48 ft.
Since its length L = 2W, substituting W = 48 into the equation, we have
L = 2(48)
L = 96 ft
Therefore the length of the room will be 96 ft.
The area of a rectangle in a two-dimensional plane is the area that it occupies. A quadrilateral, a form of two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another. It should be noted that a parallelogram also has equal and parallel opposite sides, but the angles are not exactly 90 degrees.
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Translate: 3 less than the product of 7 and a number
Answer:
3-7n
Step-by-step explanation:
Answer:6
Step-by-step explanation:
Three less than the product of 7 is 6
Just translate the sentence into a equation:7n-3=6
What is the value of k when k3 =
1
125
?
A.
1
25
B.
1
5
C.
5
D.
25
The value of k in k^3=1/125 is 1/5 (optionB)
What is Indices?Indices is the power or exponent which is raised to a number or a variable. For example, in number 2^5, 5is the index of 2 which means 2×2×2×2×2. The plural form of index is indices.
From the law of Indices,
a^-1= 1/a
similarly, 1/125= (125)^-1
from the expression, K^3= (125)^-1
K^3= (5^3)^-1
therefore K^3=(5)^-3
multiply the power of both sides by 1/3
=K^3×1/3= (5)^-3×1/3
therefore k= 5^-1=1/5
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How does decision making affect your life?.
Every decision we make is followed by a series of related events. The magnitude of the decision will determine how drastically it will affect the person making it and those around them. There is always a result, whether the impact is positive or negative.
What is the process of decision making ?Step 1: Identification of the purpose of the decision
Step 2: Information gathering
Step 3: Principles for judging the alternatives
Step 4: Brainstorm and analyze the different choices
Step 5: Evaluation of alternatives
Step 6: Select the best alternative
Step 7: Execute the decision
Step 8: Evaluate the results
When making judgments, one should always balance the potential business benefits against the drawbacks, leaning toward the former.
By doing this, potential losses to the organisation are avoided, and sustainable growth is maintained within the business. When you have to make a difficult decision, it might often seem easier to postpone doing so, especially if you encounter a lot of conflict thereafter.
However, in order to maintain control over your work and time, decisions must be made and their implications accepted.
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You want a 95% confidence interval for average pizza delivery time. A sample of 10 pizzas has an average delivery time of 34 minutes and a sample standard deviation of 5. 2 minutes. What t value do you use in your formula for the confidence interval?.
